Abstract

metal layers are calculated in the regime when size quantization of electron motion and their nonlocal contribution to conductivity play an essential role. In the THz region and in helium temperatures, this regime is realized if the thickness of metal layers is comparable to the skin-depth and metal film becomes partially transparent. Due to size quantization, the Landau damping is also quantized, leading to new resonances in surface impedances of metal film. An avoided crossing of these resonances with Fabry-Perot photonic pass bands gives rise to narrow band gaps where, nevertheless, the density of photonic states does not vanish. Such dark photonic states populating the new band gaps exhibit strongly anomalous dispersion and strong decay, as it is required by the Kramers-Kronig relations. The decay is due to the quantized Landau damping and it remains finite even in the collisionless limit.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. L. D. Landau, I. M. Lifshitz, and L. P. Pitaevskii, eds. Electrodynamics of Continuous Media (Pergamon, NY, 1984).
  2. A. B. Pippard, “The anomalous skin effect in anisotropic metals,” Proc. Roy. Soc. A 224, 273 (1954).
    [Crossref]
  3. G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. Roy. Soc. A 195, 336 (1954).
    [Crossref]
  4. L. Landau, “On the vibration of the electronic plasma,” JETP 16, 574 (1946).
  5. A. Paredes-Juárez, F. Días-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Lett. 90, 623 (2009).
    [Crossref]
  6. A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effect on optic spectrum of a periodic dielectric-metal stack,” Opt. Express 22, 7581–7586 (2014).
    [Crossref] [PubMed]
  7. A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Landau damping of electromagnetic transport via dielectric-metal superlattices,” Opt. Lett. 40, 3588–3591 (2015).
    [Crossref] [PubMed]
  8. J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
    [Crossref]
  9. S. G. Castillo-López, N. M. Makarov, and F. Pérez-Rodríguez, “Quantum resonances of Landau damping in the electromagnetic response of metallic nanoslabs,” Opt. Lett. 43, 2410–2413 (2018).
    [Crossref] [PubMed]
  10. S. G. Castillo-López, F. Pérez-Rodríguez, and N. M. Makarov, “Quantum discretization of Landau damping,” Low Temp. Phys. 44, 1606–1617 (2018).
  11. M. Y. Azbel and E. A. Kaner, “The theory of cyclotron resonance in metals,” Sov. Phys. JETP 3, 772 (1956).
  12. R. C. Jaklevic and J. Lambe, “Experimental study of quantum size effects in thin metal films by electron tunneling,” Phys. Rev. B 12, 4146 (1975).
    [Crossref]
  13. W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
    [Crossref]
  14. W. B. Su, C. S. Chang, and T. T. Tsong, “Quantum size effect on ultra-thin metallic films,” J. Phys. D: Appl. Phys. 43, 013001 (2010).
    [Crossref]
  15. I. B. Altfeder, K. A. Matveev, and D. M. Chen, “Electron fringes on a quantum wedge,” Phys. Rev. Lett. 78, 2815 (1997).
    [Crossref]
  16. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” JETP 2, 466 (1956).
  17. P. Markoš and C. Soukoulis, eds., Wave Propagation: From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, 2008).
  18. A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205 (1996).
    [Crossref]
  19. F. Peragut, L. Cerutt, A. Baranov, J. P. Hugonin, T. Taliercio, Y. De Wilde, and J. J. Greffet, “Hyperbolic metamaterials and surface plasmon polaritons,” Optica 4, 1409 (2017).
    [Crossref]
  20. H. V. Nguyen, I. An, and R. W. Collins, “Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947 (1993).
    [Crossref]
  21. R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
    [Crossref]
  22. A. A. Earp and G. B. Smith, “Evolution of plasmonic response in growing silver thin films with pre-percolation non-local conduction and emittance drop,” J. Phys. D: Appl. Phys. 44, 255102 (2011).
    [Crossref]
  23. Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
    [Crossref] [PubMed]
  24. Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
    [Crossref]
  25. C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
    [Crossref]

2018 (3)

S. G. Castillo-López, N. M. Makarov, and F. Pérez-Rodríguez, “Quantum resonances of Landau damping in the electromagnetic response of metallic nanoslabs,” Opt. Lett. 43, 2410–2413 (2018).
[Crossref] [PubMed]

S. G. Castillo-López, F. Pérez-Rodríguez, and N. M. Makarov, “Quantum discretization of Landau damping,” Low Temp. Phys. 44, 1606–1617 (2018).

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

2017 (3)

J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
[Crossref]

F. Peragut, L. Cerutt, A. Baranov, J. P. Hugonin, T. Taliercio, Y. De Wilde, and J. J. Greffet, “Hyperbolic metamaterials and surface plasmon polaritons,” Optica 4, 1409 (2017).
[Crossref]

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

2016 (1)

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

2015 (1)

2014 (2)

A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effect on optic spectrum of a periodic dielectric-metal stack,” Opt. Express 22, 7581–7586 (2014).
[Crossref] [PubMed]

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

2011 (1)

A. A. Earp and G. B. Smith, “Evolution of plasmonic response in growing silver thin films with pre-percolation non-local conduction and emittance drop,” J. Phys. D: Appl. Phys. 44, 255102 (2011).
[Crossref]

2010 (1)

W. B. Su, C. S. Chang, and T. T. Tsong, “Quantum size effect on ultra-thin metallic films,” J. Phys. D: Appl. Phys. 43, 013001 (2010).
[Crossref]

2009 (1)

A. Paredes-Juárez, F. Días-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Lett. 90, 623 (2009).
[Crossref]

1997 (1)

I. B. Altfeder, K. A. Matveev, and D. M. Chen, “Electron fringes on a quantum wedge,” Phys. Rev. Lett. 78, 2815 (1997).
[Crossref]

1996 (1)

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205 (1996).
[Crossref]

1993 (1)

H. V. Nguyen, I. An, and R. W. Collins, “Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947 (1993).
[Crossref]

1986 (1)

W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
[Crossref]

1975 (1)

R. C. Jaklevic and J. Lambe, “Experimental study of quantum size effects in thin metal films by electron tunneling,” Phys. Rev. B 12, 4146 (1975).
[Crossref]

1956 (2)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” JETP 2, 466 (1956).

M. Y. Azbel and E. A. Kaner, “The theory of cyclotron resonance in metals,” Sov. Phys. JETP 3, 772 (1956).

1954 (2)

A. B. Pippard, “The anomalous skin effect in anisotropic metals,” Proc. Roy. Soc. A 224, 273 (1954).
[Crossref]

G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. Roy. Soc. A 195, 336 (1954).
[Crossref]

1946 (1)

L. Landau, “On the vibration of the electronic plasma,” JETP 16, 574 (1946).

Altfeder, I. B.

I. B. Altfeder, K. A. Matveev, and D. M. Chen, “Electron fringes on a quantum wedge,” Phys. Rev. Lett. 78, 2815 (1997).
[Crossref]

Alù, A.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

An, I.

H. V. Nguyen, I. An, and R. W. Collins, “Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947 (1993).
[Crossref]

Azbel, M. Y.

M. Y. Azbel and E. A. Kaner, “The theory of cyclotron resonance in metals,” Sov. Phys. JETP 3, 772 (1956).

Baranov, A.

Castillo-López, S. G.

S. G. Castillo-López, N. M. Makarov, and F. Pérez-Rodríguez, “Quantum resonances of Landau damping in the electromagnetic response of metallic nanoslabs,” Opt. Lett. 43, 2410–2413 (2018).
[Crossref] [PubMed]

S. G. Castillo-López, F. Pérez-Rodríguez, and N. M. Makarov, “Quantum discretization of Landau damping,” Low Temp. Phys. 44, 1606–1617 (2018).

Cernošková, E.

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

Cerutt, L.

Chang, C. S.

W. B. Su, C. S. Chang, and T. T. Tsong, “Quantum size effect on ultra-thin metallic films,” J. Phys. D: Appl. Phys. 43, 013001 (2010).
[Crossref]

Chen, D. M.

I. B. Altfeder, K. A. Matveev, and D. M. Chen, “Electron fringes on a quantum wedge,” Phys. Rev. Lett. 78, 2815 (1997).
[Crossref]

Chen, L.-J.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Cheng, C.-W.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Collins, R. W.

H. V. Nguyen, I. An, and R. W. Collins, “Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947 (1993).
[Crossref]

De Wilde, Y.

Días-Monge, F.

A. Paredes-Juárez, F. Días-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Lett. 90, 623 (2009).
[Crossref]

Earp, A. A.

A. A. Earp and G. B. Smith, “Evolution of plasmonic response in growing silver thin films with pre-percolation non-local conduction and emittance drop,” J. Phys. D: Appl. Phys. 44, 255102 (2011).
[Crossref]

Estakhri, N. M.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Flores-Desirena, B.

Gao, J.

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

Greffet, J. J.

Gwo, S.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Halevi, P.

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205 (1996).
[Crossref]

Halperin, W. P.

W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
[Crossref]

Hugonin, J. P.

Iakushev, D. A.

Jaklevic, R. C.

R. C. Jaklevic and J. Lambe, “Experimental study of quantum size effects in thin metal films by electron tunneling,” Phys. Rev. B 12, 4146 (1975).
[Crossref]

Kaner, E. A.

M. Y. Azbel and E. A. Kaner, “The theory of cyclotron resonance in metals,” Sov. Phys. JETP 3, 772 (1956).

Khurgin, J.

J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
[Crossref]

Kim, J.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Knotek, P.

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

Krokhin, A. A.

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205 (1996).
[Crossref]

Lambe, J.

R. C. Jaklevic and J. Lambe, “Experimental study of quantum size effects in thin metal films by electron tunneling,” Phys. Rev. B 12, 4146 (1975).
[Crossref]

Landau, L.

L. Landau, “On the vibration of the electronic plasma,” JETP 16, 574 (1946).

Li, G.

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

Li, X.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Liao, Y.-J.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Liu, C.-Y.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Liu, X.-X.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Lozanova, V.

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

Makarov, N. M.

Matveev, K. A.

I. B. Altfeder, K. A. Matveev, and D. M. Chen, “Electron fringes on a quantum wedge,” Phys. Rev. Lett. 78, 2815 (1997).
[Crossref]

Nguyen, H. V.

H. V. Nguyen, I. An, and R. W. Collins, “Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947 (1993).
[Crossref]

Paredes-Juárez, A.

Peragut, F.

Pérez-Rodríguez, F.

Pippard, A. B.

A. B. Pippard, “The anomalous skin effect in anisotropic metals,” Proc. Roy. Soc. A 224, 273 (1954).
[Crossref]

Pribil, G. K.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Raja, S. S.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Reuter, G. E. H.

G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. Roy. Soc. A 195, 336 (1954).
[Crossref]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” JETP 2, 466 (1956).

Shih, C.-K.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Smith, G. B.

A. A. Earp and G. B. Smith, “Evolution of plasmonic response in growing silver thin films with pre-percolation non-local conduction and emittance drop,” J. Phys. D: Appl. Phys. 44, 255102 (2011).
[Crossref]

Sondheimer, E. H.

G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. Roy. Soc. A 195, 336 (1954).
[Crossref]

Su, W. B.

W. B. Su, C. S. Chang, and T. T. Tsong, “Quantum size effect on ultra-thin metallic films,” J. Phys. D: Appl. Phys. 43, 013001 (2010).
[Crossref]

Sun, G.

J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
[Crossref]

Taliercio, T.

Todorov, R.

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

Tsai, D. P.

J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
[Crossref]

Tsai, W.-Y.

J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
[Crossref]

Tsong, T. T.

W. B. Su, C. S. Chang, and T. T. Tsong, “Quantum size effect on ultra-thin metallic films,” J. Phys. D: Appl. Phys. 43, 013001 (2010).
[Crossref]

Vlcek, M.

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

Wang, C.-Y.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Wang, H.

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

Wang, W.

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

Wu, B.-H.

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Wu, Y.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Yang, W.

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

Zhang, C.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Zhang, M.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Zhao, Y.

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

Zhu, Y.

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

ACS Photonics (2)

J. Khurgin, W.-Y. Tsai, D. P. Tsai, and G. Sun, “Landau damping and limit to field confiment and enhancement in plasmonic dimers,” ACS Photonics 4, 2871 (2017).
[Crossref]

C.-W. Cheng, Y.-J. Liao, C.-Y. Liu, B.-H. Wu, S. S. Raja, C.-Y. Wang, X. Li, C.-K. Shih, L.-J. Chen, and S. Gwo, “Epitaxial Aluminum-on-Sapphire Films as a Plasmonic Material Platform for Ultraviolet and Full Visible Spectral Regions,” ACS Photonics,  5, 2624 (2018).
[Crossref]

Adv. Mater. (1)

Y. Wu, C. Zhang, N. M. Estakhri, Y. Zhao, J. Kim, M. Zhang, X.-X. Liu, G. K. Pribil, A. Alù, C.-K. Shih, and X. Li, “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater. 26, 6106 (2014).
[Crossref] [PubMed]

J. Phys. D: Appl. Phys. (2)

A. A. Earp and G. B. Smith, “Evolution of plasmonic response in growing silver thin films with pre-percolation non-local conduction and emittance drop,” J. Phys. D: Appl. Phys. 44, 255102 (2011).
[Crossref]

W. B. Su, C. S. Chang, and T. T. Tsong, “Quantum size effect on ultra-thin metallic films,” J. Phys. D: Appl. Phys. 43, 013001 (2010).
[Crossref]

JETP (2)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” JETP 2, 466 (1956).

L. Landau, “On the vibration of the electronic plasma,” JETP 16, 574 (1946).

JETP Lett. (1)

A. Paredes-Juárez, F. Días-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Lett. 90, 623 (2009).
[Crossref]

Low Temp. Phys. (1)

S. G. Castillo-López, F. Pérez-Rodríguez, and N. M. Makarov, “Quantum discretization of Landau damping,” Low Temp. Phys. 44, 1606–1617 (2018).

Mater. Sci. Semicond. Process. (1)

Y. Zhu, W. Wang, W. Yang, H. Wang, J. Gao, and G. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process. 54, 70 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Optica (1)

Phys. Rev. B (3)

H. V. Nguyen, I. An, and R. W. Collins, “Evolution of the optical functions of thin-film aluminum: A real-time spectroscopic ellipsometry study,” Phys. Rev. B 47, 3947 (1993).
[Crossref]

A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B 53, 1205 (1996).
[Crossref]

R. C. Jaklevic and J. Lambe, “Experimental study of quantum size effects in thin metal films by electron tunneling,” Phys. Rev. B 12, 4146 (1975).
[Crossref]

Phys. Rev. Lett. (1)

I. B. Altfeder, K. A. Matveev, and D. M. Chen, “Electron fringes on a quantum wedge,” Phys. Rev. Lett. 78, 2815 (1997).
[Crossref]

Proc. Roy. Soc. A (2)

A. B. Pippard, “The anomalous skin effect in anisotropic metals,” Proc. Roy. Soc. A 224, 273 (1954).
[Crossref]

G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. Roy. Soc. A 195, 336 (1954).
[Crossref]

Rev. Mod. Phys. (1)

W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
[Crossref]

Sov. Phys. JETP (1)

M. Y. Azbel and E. A. Kaner, “The theory of cyclotron resonance in metals,” Sov. Phys. JETP 3, 772 (1956).

Thin Solid Films (1)

R. Todorov, V. Lozanova, P. Knotek, E. Černošková, and M. Vlček, “Microstructure and ellipsometric modelling of the optical properties of very thin silver films for application in plasmonics,” Thin Solid Films 628, 22 (2017).
[Crossref]

Other (2)

L. D. Landau, I. M. Lifshitz, and L. P. Pitaevskii, eds. Electrodynamics of Continuous Media (Pergamon, NY, 1984).

P. Markoš and C. Soukoulis, eds., Wave Propagation: From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, 2008).

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Figures (6)

Fig. 1
Fig. 1 Geometry of the binary periodic stack and propagating electromagnetic wave. The stack region II is embedded between media I and III.
Fig. 2
Fig. 2 Photonic band structure (panels (a) and (b)), transmission (logT, panels (c) and (d)) and absorption (log A, panels (e) and (f)) spectra near the first dielectric Fabry-Perot resonance, Eq. (15) with j = 1. The curves on the left (right) panels were calculated for da = 447δ (da = 448.7δ).
Fig. 3
Fig. 3 Photonic band structure (panels (a) and (b)), transmission (logT, panels (c) and (d)) and absorption (log A, panels (e) and (f)) spectra near the second dielectric Fabry-Perot resonance, Eq. (15) with j = 2. The curves on the left (right) panels correspond to da = 895.8δ (da = 897.5δ). The other parameters are the same as in Fig. 2
Fig. 4
Fig. 4 Density of photonic states calculated from the dispersion relation (11). Note that the density of states does not vanish within the narrow quantum gaps at the center of the spectrum.
Fig. 5
Fig. 5 Absorption (log A) spectra of a vacuum-aluminum regular stack for three different values of the electron relaxation rate ν marked in the figure. The other parameters are the same as in the left panels of Fig. 2.
Fig. 6
Fig. 6 Electric field distribution normalized to the amplitude of the incident wave.

Equations (24)

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E a ( x ) = i k k a H a ( x a ) cos [ k a ( x b x ) ] H a ( x b ) cos [ k a ( x x a ) ] sin ( k a d a ) ,
H a ( x ) = H a ( x a ) sin [ k a ( x b x ) ] + H a ( x b ) sin [ k a ( x x a ) ] sin ( k a d a ) ,
E b ( x ) = i k d b s = H b ( x a + 1 ) cos [ k s ( x a + 1 x ) ] H b ( x b ) cos [ k s ( x x b ) ] k s 2 k 2 ε ( k s ) ,
H b ( x ) = 1 d b s = k s H b ( x a + 1 ) sin [ k s ( x a + 1 x ) ] + H b ( x b ) sin [ k s ( x x b ) ] k s 2 k 2 ε ( k s ) ,
ε ( k s ) = 1 ω p 2 ω 2 𝒬 ( k s ) .
𝒬 ( k s ) = 3 ω 4 ( k F d b π ) 1 n = N F N F 1 q n 2 / k F 2 ω ω n + | s | , n + i ν .
ω n + | s | , n = 2 m ( q n + | s | 2 q n 2 ) = ω n , s + ω s ;
ω n , s = | k s | q n m = | k s | V F q n k F , ω s = k s 2 2 m ,
0 < ω ω s < | k s | V F = | s | ( π V F / c ) ( δ / d b ) ω p .
( E ( x a + 1 ) H ( x a + 1 ) ) = M ^ ( E ( x a ) H ( x a ) ) .
M 11 = ζ 0 ζ d b cos ( k a d a ) i ζ 0 2 ζ d b 2 Z a ζ d b sin ( k a d a ) ,
M 12 = ζ 0 2 ζ d b 2 ζ d b cos ( k a d a ) + i Z a ζ 0 ζ d b sin ( k a d a ) ,
M 21 = 1 ζ d b cos ( k a d a ) + i ζ 0 Z a ζ d b sin ( k a d a ) ,
M 22 = ζ 0 ζ d b cos ( k a d a ) i Z a ζ d b sin ( k a d a ) ,
ζ 0 = i k d b s = 1 k s 2 k 2 ε ( k s ) ,
ζ d b = i k d b s = cos ( k s d b ) k s 2 k 2 ε ( k s ) .
ζ 0 ( loc ) = i ε ( 0 ) cot ( k d b ε ( 0 ) ) ,
ζ d b ( loc ) = i / ε ( 0 ) sin ( k d b ε ( 0 ) ) .
cos ( κ d ) = ζ 0 ζ d b cos ( k a d a ) i 2 Z a 2 + ζ 0 2 ζ d b 2 Z a ζ d b sin ( k a d a ) .
( t 0 ) = M ^ ( T ) ( 1 r ) , M ^ ( T ) = M ^ III M ^ I I M ^ I .
M ^ I = ( 1 1 ε I ε I ) , M ^ II = M ^ N , M ^ III = 1 2 ( 1 1 / ε III 1 1 / ε III ) .
T = | t | 2 = | M ^ 22 ( T ) | 2 , R = | r | 2 = | M ^ 21 ( T ) / M ^ 22 ( T ) | 2 , A = 1 T R .
ω j = j ( c / ε a ) π / d a where k a d a = j π ( j = 1 , 2 , 3 ) .
Re κ = p π / N d with positive integer p .

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